illustrative mathematics

Unit 1 Lesson 11 Cumulative Practice
Problems

1. Find the sum of the sequence:
a.

b.

c.

d.

e.

f.

2. Priya is walking down a long hallway. She walks halfway and stops. Then, she walks
half of the remaining distance, and stops again. She continues to stop every time she
goes half of the remaining distance.
a. What fraction of the length of the hallway will Priya have covered after she
starts and stops two times?

b. What fraction of the length of the hallway will Priya have covered after she
starts and stops four times?

c. Will Priya ever reach the end of the hallway, repeatedly starting and stopping at
half the remaining distance? Explain your thinking.

Algebra 2 Unit 1 CC BY 2019 by Illustrative Mathematics 1
Lesson 11

3. A geometric sequence starts with 10, 5, . . . Explain how you would calculate the
value of the 100th term.

(From Unit 1, Lesson 8.)

4. Here is a graph of sequence . Define recursively using
function notation.

(From Unit 1, Lesson 6.)

5. An unfolded piece of paper is 0.05 mm thick.

a. Complete the table with the thickness of the piece of

paper after it is folded in half times.

b. Define for the term. 0 0.05
1
c. What is a reasonable domain for the function ? Explain 2
how you know. 3

(From Unit 1, Lesson 9.)

Algebra 2 Unit 1 CC BY 2019 by Illustrative Mathematics 2
Lesson 11

6. A piece of paper is 0.05 mm thick.

a. Complete the table with the thickness of the paper , in
mm, after it has been folded times.

b. Does make sense? Explain how you know. 0
1
2
3

(From Unit 1, Lesson 9.)

7. An arithmetic sequence starts 84, 77, . . .
a. Define recursively.
b. Define for the term.

(From Unit 1, Lesson 10.)

Algebra 2 Unit 1 CC BY 2019 by Illustrative Mathematics 3
Lesson 11

8. Here is a pattern of growing rectangles:

a. Describe how the rectangle grows from Step 0 to Step 2.

b. Write an equation for sequence , so that is the number of squares in
Step .

c. Is a geometric sequence, an arithmetic sequence, or neither? Explain how you
know.

(From Unit 1, Lesson 10.)

Algebra 2 Unit 1 CC BY 2019 by Illustrative Mathematics 4
Lesson 11